Inference under functional proportional and common principal component models
Inference under functional proportional and common principal component models
复制标题
函数比例模型和共同主成分模型下的推理
DOI：
10.1016/j.jmva.2009.09.009
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发表时间：
2010
期刊：
影响因子：
--
通讯作者：
M. Sued
中科院分区：
文献类型：
--
作者：
G. Boente;Daniela Rodriguez;M. Sued
在许多情况下，当处理具有不同协方差算子的多个总体时，假设算子相等。通常，如果这个假设不成立，我们会分别估计每个组的协方差算子，这会导致大量的参数。在多变量设置中，这是不令人满意的，因为协方差算子可能表现出一些共同的结构。在本文中，我们讨论了扩展到功能设置的共同主成分模型，已被广泛研究时，处理多变量观测。此外，我们还考虑了比例模型，其中协方差算子被假定为等于一个乘法常数。对于这两个模型，我们提出了未知参数的估计，我们得到他们的渐近分布。还考虑了平等与相称性的检验。
In many situations, when dealing with several populations with different covariance operators, equality of the operators is assumed. Usually, if this assumption does not hold, one estimates the covariance operator of each group separately, which leads to a large number of parameters. As in the multivariate setting, this is not satisfactory since the covariance operators may exhibit some common structure. In this paper, we discuss the extension to the functional setting of the common principal component model that has been widely studied when dealing with multivariate observations. Moreover, we also consider a proportional model in which the covariance operators are assumed to be equal up to a multiplicative constant. For both models, we present estimators of the unknown parameters and we obtain their asymptotic distribution. A test for equality against proportionality is also considered.